Optimal. Leaf size=93 \[ \frac{a^8 x^5}{5}+2 a^7 b x^4+\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x+56 a^3 b^5 \log (x)-\frac{28 a^2 b^6}{x}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.110529, antiderivative size = 93, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^8 x^5}{5}+2 a^7 b x^4+\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x+56 a^3 b^5 \log (x)-\frac{28 a^2 b^6}{x}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{8} x^{5}}{5} + 2 a^{7} b x^{4} + \frac{28 a^{6} b^{2} x^{3}}{3} + 56 a^{5} b^{3} \int x\, dx + 70 a^{4} b^{4} x + 56 a^{3} b^{5} \log{\left (x \right )} - \frac{28 a^{2} b^{6}}{x} - \frac{4 a b^{7}}{x^{2}} - \frac{b^{8}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0148203, size = 93, normalized size = 1. \[ \frac{a^8 x^5}{5}+2 a^7 b x^4+\frac{28}{3} a^6 b^2 x^3+28 a^5 b^3 x^2+70 a^4 b^4 x+56 a^3 b^5 \log (x)-\frac{28 a^2 b^6}{x}-\frac{4 a b^7}{x^2}-\frac{b^8}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 88, normalized size = 1. \[ -{\frac{{b}^{8}}{3\,{x}^{3}}}-4\,{\frac{a{b}^{7}}{{x}^{2}}}-28\,{\frac{{a}^{2}{b}^{6}}{x}}+70\,{a}^{4}{b}^{4}x+28\,{a}^{5}{b}^{3}{x}^{2}+{\frac{28\,{a}^{6}{b}^{2}{x}^{3}}{3}}+2\,{a}^{7}b{x}^{4}+{\frac{{a}^{8}{x}^{5}}{5}}+56\,{a}^{3}{b}^{5}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44625, size = 116, normalized size = 1.25 \[ \frac{1}{5} \, a^{8} x^{5} + 2 \, a^{7} b x^{4} + \frac{28}{3} \, a^{6} b^{2} x^{3} + 28 \, a^{5} b^{3} x^{2} + 70 \, a^{4} b^{4} x + 56 \, a^{3} b^{5} \log \left (x\right ) - \frac{84 \, a^{2} b^{6} x^{2} + 12 \, a b^{7} x + b^{8}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.220032, size = 124, normalized size = 1.33 \[ \frac{3 \, a^{8} x^{8} + 30 \, a^{7} b x^{7} + 140 \, a^{6} b^{2} x^{6} + 420 \, a^{5} b^{3} x^{5} + 1050 \, a^{4} b^{4} x^{4} + 840 \, a^{3} b^{5} x^{3} \log \left (x\right ) - 420 \, a^{2} b^{6} x^{2} - 60 \, a b^{7} x - 5 \, b^{8}}{15 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.72184, size = 94, normalized size = 1.01 \[ \frac{a^{8} x^{5}}{5} + 2 a^{7} b x^{4} + \frac{28 a^{6} b^{2} x^{3}}{3} + 28 a^{5} b^{3} x^{2} + 70 a^{4} b^{4} x + 56 a^{3} b^{5} \log{\left (x \right )} - \frac{84 a^{2} b^{6} x^{2} + 12 a b^{7} x + b^{8}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.22438, size = 117, normalized size = 1.26 \[ \frac{1}{5} \, a^{8} x^{5} + 2 \, a^{7} b x^{4} + \frac{28}{3} \, a^{6} b^{2} x^{3} + 28 \, a^{5} b^{3} x^{2} + 70 \, a^{4} b^{4} x + 56 \, a^{3} b^{5}{\rm ln}\left ({\left | x \right |}\right ) - \frac{84 \, a^{2} b^{6} x^{2} + 12 \, a b^{7} x + b^{8}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^4,x, algorithm="giac")
[Out]